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I've seen mentioned over and over that Chapel is a phenomenal card. But I have not seen detailed instructions as to how best to use it. As a relatively new Dominion player (<30 games, ~5 with Chapel card), I've experimented with it by trashing estates at earliest opportunity and after acquiring 2 or more silvers/golds, trashing coppers. However, I haven't managed to decisively win games with it yet against opponents who aren't using it.

Chapel is a terminal action so if it shows up with another action card that can get me a silver or gold (like Militia, Smithy, Council Room, etc.) I'm more inclined to get the silver or gold, and use the Chapel later. So Chapel can actually be dead weight in the beginning which slows getting the silver or gold I need to make it useful.

There seems to be near unanimity among highly skilled Dominion players that when this card is in the game, you use it early and use it often if you want to maximize your chance of winning.

So, in detail, how does one use the Chapel card to its fullest potential?

A good answer would discuss the decision-making process when Chapel and a silver-gathering action card come up in the same 5 card hand early in the game.

Keep in mind also that it's somewhat of a different story when playing with only the Base set cards. Chapel is best when playing with the types of decks that the Base set doesn't allow. That's not to say it's not still a good card in Base set only; but it's not nearly as good as it is when you start playing with other sets.
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GendoIkariJan 10 '13 at 16:48

3 Answers
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To fully understand how to use Chapel, you have to examine its use with many different Kingdom setups. I will only detail some scenarios from the base game.

Standard Big Money Strategy

The standard Big Money Canonical strategy is to buy a Provence, else buy a Gold, else buy a Silver. To get a better understanding on how Chapel works effectively, it might be best to remove all the other complications from the deck, and examine how Chapel works to enhance the basic Big Money strategy. The first two turns will be Chapel and Silver. What are the possible 3rd/4th turns, that contain a Chapel? The table below shows the probability of getting a Chapel (Row) with different distributions of Copper (C), Silver (S), or Estate (E). Your other hand (Column), and its dollar worth are also displayed. (There is a 1/6th chance that you don't get Chapel until your 5th turn). These figures agree with my calculations, so I hope that means I didn't make any mistake.

If you compare the results of the Chapel Canonical is a deck of usually 10-9 cards, with a small 16.7% chance of not having drawn Chapel until Turn 5 (To mitigate this, it might be worth it to buy a Chapel during Turn 3 when you only have a $2 hand. I haven't worked out the exact math, but it looks like there is a ~0.8% chance that you draw Chapel 5th turn and only had a $2 Turn 3 hand, compared to a ~2% chance of having a $2 Turn 3 and drawing Chapel Turn 4. I think it is worth the risk of buying Chapel Turn 3 on a $2 hand to mitigate a slow Turn 5 Chapel Start. It is unlikely that you draw 2 Chapels Turn 5, so you should be able to shrink your deck by Turn 7-8 with the extra Chapel).

On Turn 5, the deck will usually consist of 2 Silver, 2 Estates (23% chance of Trashing 2), 4-5 Copper, and your Chapel. A Big Money Canonical deck will usually have 14 cards. It will consist of 4 Silvers (~28% chance of 1 Gold in place), 3 Estates, and 7 Copper. The most important goal for both of these decks is to hit that magical $6 hand. Starting with Turn 5/6, the Chapel deck should be able to pull this off more often. The Chapel deck should be able to buy a Gold during Turn 5/6, and should be able to remove another 4-2 cards. This will setup their Turn 7/8 with a 8-7 card deck that consists of 1 Gold, 2 Silver, 1-0 Estate, 4-3 Copper. From that point onward, the Chapel deck should consistently be able to buy Gold, if not a Provence. Big Money on the other hand keeps increasing the size of their deck. They draw their own Gold less often, and have a much higher chance of drawing the Gold with Estates (making it difficult to hit $6 or $8). It is important to note that by Chapeling away your Estates, you are 3 Points down from your opponent. It is vitally important to modify this canonical simplistic strategy to take into account the number of Provinces left, the current VP deficit, and which other Kingdom cards are available.

Thief (Treasure Stealers)

A Chapel strategy is very risky with Thief available in the Kingdom cards. Removing the chaff from your deck increases the likelihood that your opponent hits your Gold/Silver. This is especially true in mulitplayer where you will be subject to multiple attacks.

Workshop and Gardens (Quick Piles)

Ignore your Chapel strategy, it is too slow. Your opponents will increase the size of their decks making their Gardens worth 2-3VP, and will end the game on piles before you get your money building Province buying engine online.

Militia (Hand Destruction)

Chapel works because of its ability to remove chaff from a hand with Chapel in it. Any card that shrinks your hand size reduces the effectiveness of Chapel, reducing the trashing from a maximum of 4 to 2. A Chapel strategy gets considerably weaker in multiplayer, with multiple opponents able to attack you.

In general, it is preferable to not Chapel if you have another action card in your hand that would gain you a Gold/Province if you played it. Your first two turns will likely be Chapel/Silver, unless a really good $4/$3 card is available (Militia in a 2-Player game is very good, and shouldn't hurt a Chapel strategy game too badly). Good examples of this are Chancellor/Bureaucrat, or any other card that gains you $2. Even a card like Remodel can supplement a Chapel strategy, and turn that Chapel into a Remodel mid-game, and eventually into Golds/Duchies. The sixth of a time that you get a $5/$2 split, you should probably by a $5-card instead of a Silver. No $5 is worse than a Silver.

Mid-game, when your deck has dwindled, you should almost always play the action card. This is especially true if you are unable to trash 2-3 Coppers/Estates.

@ColinD, thanks. I think I still need the possible deck contents of Big Money on Turn 5-6, so that I can show how much more efficient Chapel is at hitting $6/$8. I also found a small calculation error that I will correct when the BMC numbers are finalized.
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user1873Jan 12 '13 at 1:43

One important thing to keep in mind with Chapel is that it only really shines when it can be used to play important Actions frequently. A naive Chapel into Silver+Gold strategy is surprisingly weak to many players who have lost to powerful Chapel decks; you spend too long trashing cards instead of buying money and end up with a deck that quickly chokes on Victory cards.

Simulations of Chapel decks indicate that a basic Chapel + money-buying strategy loses 2/3 of the time to a money-buying strategy without Chapel. (The "BMU" the linked page refers to is Big Money Ultimate, a money strategy that uses a well-tuned heuristic to buy Duchy and Estate as appropriate near the end of the game.) Making Lab available improves the Chapel deck's win ratio to only about 1/2; Lab benefits from a powerful, thin deck, but not enough to make the strategy dominant.

It is important to compare like to like. Chapel Canonial is most similar to BMC (Big Money Canonical) and Chapel scores 49% vs. it. Both strategies are "dumb" not taking into account Provinces left, etc. Single Chapel 1 more closely resembles BMU (Big Money Ultimate), and wins 55%. Both of these strategies modify their buys based upon Proviences left and other factors.
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user1873Jan 10 '13 at 3:44

Chapel can be effectively used mid and late game, but that requires card draw or action branching or both.

The trick to chapel is to trash lots of cards with it early and not rely on it late game (turn 10 bad mid-late game cards into 1 dead card early). This means trashing your entire starting deck as soon as possible. Do not wait until you have plenty of silver + gold to trash coppers. You should consider trashing coppers immediately and buy 2 silvers (or something to get you to at least $3) when not trashing 4 cards.

Ideally using the above strategy you will end up with a deck <= 5 cards that contains 1 chapel and 2 silvers (or 2 cards that will make your hand >=$3 each turn). From here you have slim deck that can be quickly transformed to use whatever actions you want from the supply. The next couple of buys you make will see use almost immediately, while your opponents will each have a couple of hands before new cards get to see use.

If you hold off on trashing until later in the game, you are going to have to deal with the following situations:
1. drawing chapel when you do not draw anything you want to trash.
2. drawing chapel when you have a different action in your hand you want to play.

Agreed - chapel is a game winner if you can get rid of your starting deck by turn 5 or 6.
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Charles BoyungJan 9 '13 at 18:45

As a point of clarification, are you suggesting that you buy a Chapel and no other action cards until you have 2 silvers? You sort of implied that but I wasn't sure.
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Joe GoltonJan 9 '13 at 19:31

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@JoeGolton - YES! Your first two turns should be chapel/silver. Then on your third or fourth turn, you will chapel away anything that isn't a silver. On the turn where you don't draw your chapel, you are buying another silver. Fifth turn (or at worst, 6th turn) you are using chapel again. On the turn when you aren't using chapel there, you start buying what makes the most sense based on what is on the board.
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Charles BoyungJan 9 '13 at 20:12

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@JoeGolton - Unless the other action card also gives you $2 when played, and there is only one. More or less. You do not want to run the risk that you trash most your coins but then have difficulty buying even silver. So silvers are the safest bet initially.
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Jirka HanikaJan 9 '13 at 20:13

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@JoeGolton You want your first couple of trashes/buys to put you in a position where you will never have a bad hand afterwards. having 2 silvers will guarantee you a 3rd which in turn guarantees you a gold. terminal actions will collide often in a small deck, so they are not worth picking up until you want to play them instead of playing chapel.
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Colin DJan 9 '13 at 20:24